You choose your Stable location when you set up your Stable (best locations are near the NY tracks, especially Aqueduct or Belmont). You want to choose a location where you won't have to spend a lot of money shipping your horses to tracks to race.

To the best of my knowledge, it isn't easy to change Stable location once you are set up. I believe Shanthi would need to do it manually. For a new stable like yours, it might not be as difficult, however, for a large Stable like mine, I suspect it would take her quite a while to do.